4430
Journal of the American Chemical Society
Based on X - a scattered wave calculations1 and the eclipsed structure of Re2C14(PEt&,I2 the ground-state electronic configuration is thought to be ( c T ) ~ ( T ) ~ ( S ) * ( S * ) ~ .Reduction of NO+ to N O requires the addition of an electron to one of the empty "*NO orbitals. However, if this electron transfer were effected by direct end-on binding of N O + to one of the empty, axial positions of the Re2X4(PR3)4 dimer, then a typical HOMO-LUMO electron transfer does not appear possible because the net overlap between the 6*metal and T * N O orbitals must, by symmetry, be zero. Therefore, the mechanism of the electron transfer warrants further investigation. It may be that transfer occurs from one of the filled rrnetal orbitals followed by "relaxation" of an electron from the filled1,,,6,* orbital to the orbital.
Acknowledgments. W e are grateful to the National Science Foundation (Grant CHE74-12788A02) for generous support of this research and the Camille and Henry Dreyfus Foundation for the award of a Teacher-Scholar Grant to R.A.W. References and Notes (1) F. A. Cotton, Chem. SOC.Rev., 27 (1975), and references cited therein. (2) F. A. Cotton, Acc. Chem. Res., in press, and references cited therein. (3) F. Hug, W. Mowat, A. Shortland, A. C. Skapski, and G. Wilkinson, Chem. Commun., 1079 (1971). (4) M. H. Chisholm, F. A. Cotton, M. Extine, and B. R. Stults, J. Am. Chem. Soc., 98, 4683 (1976). (5) F. A. Cotton, B. R. Stults, J. M. Troup, M. H. Chisholm, and M. Extine, J. Am. Chem. SOC.,97, 1242 (1975). (6) M. H. Chisholm, F. A. Cotton, B. A. Frenz, and L. Shive, J. Chem. Soc., Chem. Commun., 480 (1974). (7) M. H. Chisholm, F. A. Cotton, M. W. Extine, and B. R. Stults, Inorg. Chem., 16, 603 (1977). (8) M. H. Chisholm, F. A. Cotton, C. A. Murillo, and W. W. Reichert, Inorg. Chem., 16, 1801 (1977). (9) J. R. Ebner and R. A. Walton, Inorg. Chem., 14, 1987 (1975). (IO) H. D. Giicksman and R. A. Walton, Inorg. Chem., submitted for publication. (11) F. A. Cotton and G. G. Stanley, to be published. (12) F. A. Cotton, B. A. Frenz, J. R. Ebner, and R. A. Walton, Inorg. Chem., 15,
1 100:14 /
July 5, 1978
1630 (1976). (13) F. A. Cotton and B. M. Foxman, Inorg. Chem., 7, 2135 (1968). (14) R. B. King, Coord. Chem. Rev., 20, 155 (1976). (15) R. J. Klingler, W. Butler, and M. D. Curtis, J. Am. Chem. SOC.,97, 3535 (1975). (16) D. S.Ginley, C. R. Bock, and M. S. Wrighton, Inorg. Chim. Acta, 23, 85 (1977). (17) J. Potenza, P. Giordano, D. Mastropaoio, and A. Efraty, lnorg. Chem., 13, 2540 (1974). (18) C. A. Hertzer, M.S. Thesis, Purdue University, 1977. (19) C. A. Hertzer and R. A. Walton, Inorg. Chim. Acta, 22, L10 (1977). 100, 991 (1978). (20) D. J. Salmon and R. A. Walton, J. Am. Chem. SOC., (21) F. A. Cotton, N. F. Curtis. and W. R. Robinson, Inorg. Chem., 4, 1696 (1965). (22) C. A. Hertzer. R. E. Myers, P. Brant, and R. A. Walton, Inorg. Chem., in press. (23) P. G. Douglas and B. L. Shaw, J. Chem. SOC.A, 1491 (1969). (24) A€, N 60 mV and ip,alip,c 1; see R. W. Murray and C. N. Reilley, "Electroanalytical Principles", Interscience, New York, N.Y., 1963. (25) F. A. Cotton and E. Pedersen, J. Am. Chem. Soc., 97, 303 (1975). (26) E means an electrochemical reaction, either an oxidation or a reduction, while C means a chemical reaction. Thus an EC reaction would be an electrode process followed by a chemical reaction. Rate of disappearance of Re2X4(PR3)4was determined by monitoring the reaction by cyclic voltammetry and using the resulting peak heights as a measure of concentration. This is done by using the Randles-Sevcik equation.28 Full details of a similar determination can be found elsewhere.29 R. N. Adams. "Electrochemistry at Solid Electrodes", Marcel Dekker, New York, N.Y.. 1968, p 124. D. J. Salmon, Ph.D. Dissertation, The University of North Carolina, Chapel Hill. 1976. DD 96-106. M. T. Mocek, M. S. Okamoto. and E. Kent Barefield, Synth. React. Inorg. Mt.-Org. Chem., 4, 69 (1974). The estimate of the oxidizing power of NO+ is referenced to the Ag/AgCi electrode. Since the difference between the Ag/AgCI electrode and the calomel electrode is small,31when considering this estimate no conversion is necessary. See, C. K. Mann and K. K. Barnes, "Electrochemical Reactions in Nonaqueous Systems", Marcel Dekker, New York, N.Y., 1970, and references cited therein. J. R. Ebner and R. A. Walton, inorg. Chem., 14, 2289 (1975). J. Chatt, C. M. Elson, N. E. Hooper, and G. J. Leigh, J. Chem. SOC., Dalton Trans., 2392 (1975). M. Peiavin, D. N. Hendrickson. J. M. Hollander, and W. L. Jolly, J. Phys. Chem., 74, 1116(1970). J. R. Ebner and R. A. Walton, Inorg. Chim. Acta, 14, L45 (1975). F. A. Cotton, P. E. Fanwick, L. D. Gage, B. Kalbacher, and D. S. Martin, J. Am. Chem. SOC., 99,5642 (1977).
Oxygen- 17 Nuclear Magnetic Resonance Studies on Bound Water in Manganese( 11)-Adenosine Diphosphate Mark S. Zetter, Grace Y-S Lo, Harold W. Dodgen, and John P. Hunt* Contributionfrom the Department of Chemistry, Washington State Unicersity, Pullman, Washington 99164. Received September I , 1977
Abstract: Oxygen-I 7 line broadening and shift measurements have been made on aqueous solutions containing manganeseADP complexes. Mono and bis complexes a r e considered. Log K Z (K2 = [ML2]/(ML] [ L ] ) is ca. 2.6 at 25 "C and AH2 is ca. - I kcal/mol. The mono complex appears to have four bound waters which are kinetically equivalent. The bis complex appears to have three or four bound waters suggesting that it is not the usual sort of bis complex but a stacked one. The kinetics of water ~~-, and M I I ( A D P ) ~ ( H ~ O ) Im~~-. exchange are not greatly different for Mn(H20)62+, M ~ I ( A T P ) ( H ~ O ) Mn(ADP)(H20)4-, plications of the results a r e discussed in regard to mechanisms, N M R and EPR studies, and structures. The work supports the validity of using precise measurements of small shifts to determine numbers of bound water molecules.
Many enzymic trans-phosphorylation reactions involving A T P (adenosine triphosphate) and A D P (adenosine diphosphate) require divalent metal ions as cofactors. Consequently, the interactions of such metal ions with nucleotides, particularly ATP, have been the subject of numerous studies, most of which have been discussed in the reviews by Phillips' and Izatt et a1.2 Metal-adenosine diphosphate complexes have received considerably less attention than similar ATP complexes. In this paper we report on Mn(I1)-ADP, a complex which is impor0002-786317811500-4430$01 .OO/O
tant as a leaving group in many in vitro enzyme studies. This complex has been studied by Cohn and hug he^,^ who found that both the a and 6 phosphate groups were bound to the manganese. They reported also that manganese interacts with the adenine ring, although the authors recognized that their large [ADP]total- [ Mn] ratio could produce complexes other than MnADP- which might be responsible for the observed interaction. ( I n this connection Frey and Stuehr4 have shown that the stability constant for the Ni(ADP)24- complex is of the order of l o 2 M-I.)
0 1978 American Chemical Society
Hunt et al.
/ Manganese(II1-Adenosine Diphosphate
Table 1. Composition of Solutions at 25 Solution NO. 1 2 3 4 5 6 7 8
“c
Total Mn Total x 1 0 3 ~ ADPX 1 0 3 ~ 1.948 2. I48 2.102 2.180 1.572 4.030 6.033 3.096
443 1
2.240 4.771 7.131 10.16 0.857 4.740 19.30
PH 8.16 7.90 7.95 7.96 7.82 8.41 8.06 3
Oxygen-17 N M R has been used extensively in this laboratory to study paramagnetic ions and their complexe~.~ By using this technique and under favorable conditions, it should be possible to obtain an estimate of the number of waters bound, and therefore the number of ADP binding sites, in the solvated MnADP- complex and to determine whether or not these waters are kinetically equivalent.6 Both of these determinations will be relevant to the nature of the Mn-adenine ring interaction. Further, by examining the effect that varying Mnt,,,l-ADPt,,,~ ratios have on the observed I7O line broadening, it may be possible to obtain information on a bis complex, Mn(ADP)24-, if its formation constant is sufficiently high. Oxygen- 17 N M R also has proven to be an excellent method for determining the rate constant for water exchange ( k e x ) between waters bound to a paramagnetic complex or ion and bulk water. A comparison of k,, for the MnADP- complex with the rate constant for the substitution of the 8-hydroxyquinoline anion (Ox-) into the same complex to form OxMnADP2- should provide adequate information to determine whether water exchange or some other process is rate determining in ternary complex formation. Such comparisons have proved particularly useful in the case of the MnATP2c~mplex.~
Experimental Section Reagents. I7O h a t e r (7 and 18 atom %, normal H content) was obtained from Y E D A R & D Co., Ltd., Rehovoth, Israel. It was redistilled in vacuo before each use. Manganese chloride ( M n C 1 ~ 4 H 2 0 ; Mallinckrodt AR grade), zinc chloride (ZnCl2; Baker A R grade), and magnesium nitrate ( M g ( N O i ) r 6 H 2 0 ) ; Mallinckrodt AR grade) were used without further purification. Solutions of these salts, in normal water, were standardized by EDTA titration. A D P was obtained as the lithium salt (Li3ADP) from Schwarz Bioresearch Inc. Analysis of the A D P by paper chromatography in an isobutyric acid-ammonia-water (66: I :3) mixture gave -2% A M P content and a negligible A T P content. The inorganic phosphate content, as determined by the method of Rockstein and Herron,8 was approximately 2%. Solutions of Li3ADP in normal water were standardized spectrophotometrically at 259 nm and by acid-base titration. These solutions were kept frozen when not in use. Preparation of ”OH2 Solutions. Aliquots of the standard manganese and A D P solutions were mixed in a IO-mm diameter glass tube and normal water was added to give a total volume of -1 .O mL. The pH of the solution was adjusted to ca. 8 by adding either concentrated N a O H or HCI. The water was evaporated in vacuo a t room temperature, I .O mL of 18% enriched I7OH2 was added to the remaining solid, and the pH was measured on a Beckman Research p H meter equipped with a microcombination electrode. (In some cases the p H was measured on a “dummy” solution prepared in an identical manner to the I7O solution, but with normal water). T h e sample tube was sealed under -400 m m of pressure of “prepurified” nitrogen. The compositions of all the solutions used are given in Table I. Blank solutions for the shift and line broadening measurements contained zinc (solutions 1-4) or magnesium (solution 5) in place of manganese. Otherwise they were identical in composition and p H (to within 1 0 . 1 pH units) to the corresponding sample solution. N M R Line-Broadening Measurements. Line-broadening mea-
[Mn2+] 1 0 5 ~
x
9.13 1.53 0.657 0.379 (73.0) 15.8 0.966 309.6
[MnADP-] x 105 M 171 133 94.2 73.7 (83.9) 34 1 183
[Mn(ADP)z4-1 x1 0 5 ~ 14.8 80.2 115 144 (0.353) 46.5 419
Ionic strength 0.009 0.023 0.036 0.052 0.005 0.018 0.099
surements were made on solutions 1-5 with the N M R spectrometer in the configuration described p r e v i o ~ s l yLow-frequency .~~~~ ( 1 5 Hz) square-wave modulation and a locked frequency of 11.5 or 5.75 M H z were used. At these frequencies the I7O resonance signal was observed at ca. 20 or 10 kG, respectively. The spectra were recorded on a X-Y recorder and the full width a t half-height was measured by conventional “pen-ruler” techniques. Two upfield and two downfield sweeps were recorded a t each temperature. The average standard deviation in line width was 3.6 and 4.3% respectively for the high- and low-field data. The line width measurement was reversible with respect to temperature; this served as a check of the temperature stability of each solution. When hydrolysis of the A D P occurred, it was accompanied by a decrease in line width. Chemical Shift Measurements. The measurement of useful 170 shifts for manganese(I1) systems at temperatures less than 100 “ C is difficult since the line broadening to shift ratio is generally very high. However, changes in our N M R instrumentation (made after the line widths were measured) have allowed us to make reasonably precise shift measurements on the Mn(I1)-ADP system. Briefly, the magnetic field has been locked by using as an “error” signal the proton resonance of mineral oil, and it is stable to ca. 0.1 ppm. Resonances were obtained by linear frequency sweeping. Frequency reference marks are generated at intervals of 10% of the frequency span. When required, signal averaging was used to increase the signal-to-noise ratio. The starting and finishing frequency of a scan a r e known precisely, and the frequency of the resonance line can be measured to better than 0.1% of the frequency scan width by using a Lorentzian curve synthesizer. The experimental Lorentzian line, which is stored in a Fabritek signal averager, is displayed on a 20 in. oscilloscope simultaneously with a continuously adjustable synthetic Lorentzian curve produced by an analog device. The height, width, and position of the synthetic curve a r e adjusted until the “best” visual fit to the experimental curve is obtained. The position (frequency of resonance) and line width can then be read from the previously calibrated synthesizer controls. The advantages of similar comparative measuring techniques, as applied to exponential curves, have been discussed previously.” One added advantage of the present system, though, is that the intermediate storing of the experimental trace on the Fabritek allows measurement of the spectra as soon as they are recorded. Such analog systems offer an inexpensive, but still rapid, alternative to on-line digital computer methods. Precision of fitting is better than 1 1 % on low-noise curves; the trained eye is an extremely good averager. Paramagnetic shifts for the Mn-ADP system were measured on solutions 6 and 7 at a frequency of 1 1.5 MHz. The resonance frequency of bulk water in the presence (Oobsd) and absence (00;the zinc or magnesium blank solution) of paramagnetic ions was measured by the method outlined above. Measurements were made at 60 “ C , where the shift was almost at its limiting fast exchange value, and at -4.8 “C, where the shift was near zero (slow exchange region). These temperatures were chosen to be as far away from the temperature of maximum broadening as experimentally possible, the high-temperature limit being set by solution stability considerations. Also, paramagnetic shifts were measured for the aquo manganese(l1) ion, solution 8. The concentration of Mn2+ and the temperatures at which the shifts were measured were chosen so that the shift and line broadening would be as close as possible to that produced by the Mn-ADP system. In this way a comparison of the measured Mn’+ shift with that measured in the same system (see Figure 1) at very high temperatures (160-1 80 “ C ) provided a measure of the reliability of the Mn-ADP system shift data. (The shift for MnZ+can be measured
Journal of the American Chemical Society
4432
100:14
/ July 5 , 1978
effects of which we are aware for water exchange; nor is a saturation effect expected. At the maximum in the Bmolcurves, T I ,makes its largest relative contribution and Bmol decreases with decreasing magnetic field at every ADP3- concentration. T I ,can be described by the equation12
50
30
2.3
/
2.5
2.7
2.9
3.1
10'1~
(K")
Figure 1. Line broadening and shift data for
3.3
3.5
3.
Mn(H20)6*+.
much more accurately a t these high temperatures since the line broadening is decreased much more rapidly than the limiting shift as the temperature is increased). The data in Figure 1 were obtained over a wide range of p H and concentrations and using different experimental techniques. They will be discussed in detail in a separate paper.
Results and Data Treatment Line Broadening. Equilibrium Considerations.The untreated experimental line broadening data of 11.5 and 5.75 M H z are shown in Figure 2. Figure 3 shows the same high-frequency data, but here they are smoothed and plotted as the line broadening produced per mole of total manganese, Bmol,vs. temperature. The decrease in BmoI as the [ADP]tota~-[Mltota~ ratio increases is real and indicates that at least two broadening species are present in solution. It can be shown qualitatively that the data cannot be accounted for by assuming that these species are Mn2+ and MnADP-, as follows: At low temperatures, Bmolis greater than that if all the manganese were present as Mn(H20)62+ on a per mole basis. As the [ADPItotal- [MnItotalratio increases, the [ MnADP-] -[Mn2+] ratio should increase, and so the line broadening should also increase. In fact, Bmoldecreases and a simple Mn2+/MnADPmodel, therefore, can be discounted. Computer fitting treatments confirm that this model cannot account for the data a t low temperatures. However, a t high temperatures this model is workable, but the stability constant for the MnADP- complex would have to be considerably smaller (log K = 3.5) than any of the published (ca. 5 ) in order to fit the data. If, as expected from reported stability constants, the mono complex is essentially completely formed in solution 1, how can one explain the decrease in Bmol with increasing ADP-Mn ratios? The factors which control the line broadening (see later discussion) are Tie, n (number of bound waters), and T~ (mean life for water exchange). At low temperatures, the line broadening is mainly controlled by n/Tm. If n decreases, a bis complex is implicated. If T~ increases with no bis complex formed, one would have to say that excess ligand slows the water exchange rate by some medium effect contrary to any
where A is a parameter measuring the amplitude of modulation of the zero-field splitting, T is the correlation time for the modulation, and ws is the ESR frequency (rad/s). A decrease in Bmolwith decreasing field requires W ~ T> 1 which in turn leads to the conclusion that T I ,is proportional to T . If the only effect of increasing ADP3- concentration is to increase the viscosity of the solutions and not form any complex species beyond the mono complex, T would increase, T I , would increase, and Bmolwould increase. This is contrary to what is observed. A reasonable interpretation of the data can be made assuming that the relevant species are Mn2+, MnADP-, and Mn(ADP)24-. The nature of the bis complex is not specified at this point except to assume that some water is still bound to manganese. Thus, at the pH's used, the following equilibrium constants were sufficient to define the distribution of species: [LiADP2-] [HADP2-] KH = K L= ~ [ADP3-] [Li+] [ADP3-] [H+] [Mn(ADP24-] [M n ADP-] K2 = K1 =[ADP3-] [MnADP-] [ADP3-] [ Mn2+] The literature values used for these constants are log K H (25 O C , I = O ) = 7 . 2 0 ; ' 3 1 0 g K ~ , ( 2 5" C , 1 = 0 . 2 ) = 1.15;1410gK1 (25 OC, I = 0.0085) = 4.98.15 The corresponding enthalpies A" and AH1 were taken as 1.3 kcal16 and 2.6 kcal,15 respectively. AHL, was assumed to be the same as that for A". No literature data are available for K z , but a rough preliminary treatment of the data showed log K2 = 2.5 a t 25 "C. The ionic strength dependence of K H ,KL], and K1 was calculated from the following equations:
+ 3.841 log K L = ~ 1.52 - 2.54(11/2)+ 3.841 log K H = 7.20 - 2.54(11/2)
log K1 = 5.43 - 4.06(11/2) 6.361 - 2.04(11/2)/1
+
+ 6.02(Z'/2)
(1)
(11) (111)
Equation I was obtained from Phillips et al.I3 The ionic strength dependence of K L ]was assumed to be the same as that for KH. Equation I11 was also obtained from Phillips et al." They derived this equation for MgADP- from their measured activity coefficient ratios for protonated and deprotonated A M P and A D P species. The thermodynamic constants K O 1 and K'L, used in equations I1 and 111were calculated from the K1 and KL, values given above a t I = 0.0085 and 0.2, respectively. The ionic strength of each solution, as given in Table I, was calculated by a computerized iterative procedure with the above equilibrium constants and equations. Log K2 was assumed to be 2.5 in these calculations. Line Broadening. Quantitative Treatment. The line-broadening data are generally described in terms of the SwiftConnick equation.'* For manganese systems this equation can be simplified to the form'
Here A is the observed paramagnetic contribution to the line broadening (measured from full width a t half-height) in Hz;
Hunt et al.
4433
/ Manganese(II)-Adenosine Diphosphate 3
SOLUTION
SOLUTION
2.0
I
t
0.2
3.0
3.4
3.2
3.6
1
3.0
3.2
io3 -
T
3.4
io3 T
3.6
Figure 2. Semilogarithmic plot of the observed paramagnetic line broadening, A,vs. 1 / T for solutions 1-4. 0 and 0 represent the data at 11.5 MHz and 5.75 MHz, respectively. The full lines are the computed best fits to the data (see text), as calculated from the results in Table 11.
I/T, is the water exchange rate constant, k e x ,in s-l; T I , is the longitudinal electronic relation time in s; n is the number of (equivalent) waters bound in the metal’s inner coordination sphere; C = ‘/3(S)(S l ) ( A / f ~ where ) ~ , S is the electron spin for manganese(I1) (5/2) and A / h is the scalar coupling constant in rad s-’. k,, can be expressed by the transition state theory equation as
140
+
+ AS*/R)
k,, = kT/h exp(-AH*/RT
(V)
T I , is the only field-dependent term in eq IV, and it was taken to be independent of temperature because of the short range over which it is important, leaving 7, as the only temperature-dependent term. If n is unknown a more convenient form of eq IV is T ’ z ~= 55.5
[
1 +(” + k)] n2C 7,
900 800
-
700
.=
I
600
Y /
m 500L
(VI)
Thus, T’2pcan be defined by four variables, nA/h, TI&, AH*, and AS* for n/7,. Now the broadening produced by each solution at any given temperature, A, can be expressed as (assuming no coupled exchange)
+
405 302 . 9
A3.c )
I
3.2
31
IO’/T
I
33 (K-’)
I
I
3.4
3.5
a
Figure 3. Semilogarithmic plot of the paramagnetic line broadening per A =AM~[M~A ] M~ADP[M~ADP-] mole of total manganese, B,,I, vs. 1 / T . From top to bottom the lines -k A M ~ ( A D P ) ~ [ M ~ ( A D (VII) ~ ) ~ ~ - I represent hand-smoothed data for Mn(Hz0)62+ and solutions 1-4, re-
where the Ameta]species terms are the broadening produced per mole. Since from eq IV 1/ T ’ Z P~ = A/ [metal species] 7r r=O
T 2 p ( Mn(ADP),
]
(VIII)
This is the equation used to treat all the line-broadening data. T’2p(Mn) can be calculated from the previous work on the Mn(H20)62+ system (see Figure 1 ) . K H ,K L ~and , K1 can be calculated a t any ionic strength and temperature from the
spectively.
information given above, and these constants together with assumed values for K2 and AH2 can be used to calculate the species concentrations. Thus there are ten unknowns involved in eqVII: AH*, AS*,Tl,/n, and nA/h for both MnADP- and M I I ( A D P ) ~ ~ -and , K2 and AH2. No account could be taken of the possible ionic strength dependences of K2 or 7,.
4434
/ 100: I4 / July 5 , I978
Journal of the American Chemical Society
I
I
,
I
.
SoLuT‘oN’
1
2.01
Table 11. Computed N M R , Equilibrium, and Kinetic Parameters“ for Mn-ADP System At 11.5 M H z At 5.75 M H z For For For MnFor MnMnADPMnADP- (ADP)z4-
I O c IYI ,
.
-
a 0,
1
3
aoa-
0.2
34
32
30
36
1
103 -
T
Figure 4. Semilogarithmic plot of the observed paramagnetic line broadening, A , vs. l / T for solution 5. 0 and 0 represent the data at 11.5 and
5.75 MHz, respectively. The full lines are calculated from results in Table 11.
AH* (for n / T , ) , 8.6 f 0.6 kcal/mol AS* (for n / ~ ~ , , ) , 9.1 f 2.3 eu T,,/n, s x 10’ 3.9 f 1.9 (25 “C) n.4/h, MHz 21.6 f 3.0
9.1 f 1.3 8.5 f 1.3 9.4 f 2.5 9.9 f 5.0 9.2 f 5.4 9.9 f 9.6 3.8 f 2.6
1.9 f 2.1
16.3 f 3.9 22.1 f 9.2 12.3 f 6.8
- 1.5 f 2.9 2.64 f 0.16
AH2, kcal/mol Loa K , (25 ‘C)
5.8 f 8.9
-0.8 f 4.5 2.64 f 0.33
Errors are linear estimates of the standard deviation
Therefore, eq IX can be written as
Q = Qlim * P All the data from solutions 1-4 a t one frequency were treated simultaneously with a slightly modified form of the nonlinear least-squares program of Dye and N i ~ e 1 y . The I~ modification allowed the program to “recognize” the chemical solution from which each data point came. Then using the appropriate enthalpies and ionic strength corrections to calculate K i , K H , and K L ~it, calculated Mn*+, MnADP-, and Mn(ADP)24- from the pH, total species concentrations, and its current best estimates for K2 and AH2. The sum of the residuals was then calculated in the usual manner. Very good initial estimates were required for convergence, not surprising with ten unknowns. The data a t both frequencies were fitted completely independently in this manner, and the results are summarized in Table 11. Generally, the agreement between the two sets of data is excellent. The solid lines in Figure 2 represent the computer fits to the data. It is worth reemphasizing that all the data for solutions 1-4 for a given frequency were fitted “simultaneously” to give the best overall fit to the data; this accounts for the fact that a fit for a given solution might not appear the best possible. The fits for the low-frequency data are satisfactory, while those for the more precise high-frequency data are excellent. The Mn2+/MnADP-/ Mn(ADP)24- model therefore is consistent with these data and assumptions. The data for solution 5 are plotted in Figure 4. The full lines, computed by using the results in Table 11, do not fit the data as well. Possible explanations are given later in the discussion section. Shift Data. The Swift-Connick equation for the paramagnetic shift may be expressed as Q-
TS[H20] --nTAw, [metal species] wo
Here wo and a,,,( w = 2 x v ) are the resonance frequencies of bulk water and metal-bound water, respectively, Awm = (am - 00) = (w,, - wobsd) and S is the fractional observed innersphere shift (W&,sd - q ) / w o , where wobsd is the observed resonance frequency of bulk water in the paramagnetic solution. T?,,,equals (1 / C ) (1 / T ~ 1/Tie) for manganese. Also, for Mn (T,Ac+,)* > T,, eq IX can be reduced to the limiting form:
+
where
+
(XI)
+
P = 1/( 1 2Tm/ T 2 m T m 2 / T2m2) (XII) The scalar coupling constant, A/h, may be defined as (XIII) Here, k is the Boltzmann constant; y2yis the nuclear magnetogyric ratio; S is the electronic spin; p is the Bohr magneton in cgs units; and geffis the electron g factor (taken to be the “spin-only” value of 2.0). For manganese(I1) this equation reduces to: A/h = Qllm X 1.47 (MHz)
(XIV
n
The total measured fractional shift, S , can be expressed as S’ = S M n + S m + S b + S b u l k + S o u t e r where SMn,Sm,and Sb are the shifts attributable to Mn(H20)62$, MnADP-, and Mn(ADP)14-, respectively. Sbulk and S O U t e r are shifts arising from bulk susceptibility effects and second-coordination or outer-sphere effects, respectively. With the subscripts h and I representing respectively the higher and lower temperatures used to measure the shifts, the following equation holds:
+
+
(ThSh - TiSl) = ~ ‘ \ , ( S I J S~h ” ”’ Shb) - Tl(Si‘” f SI’” -k Sib) ( ThShbUlk - bulk) + (ThShouter- 7’lSloutcr
+
1
(XV)
If the exchange of the outer-sphere waters is assumed to be fast, then Q(outer) should be at its limiting value throughout the entire temperature range used in this study. Further, the bulk susceptibility shift follows a Curie law type dependence with temperature. Thus, T h S h o u t e r = 7‘ISIOUter and T h S h b U l k = T , S l b u l k and since from eq 1X T S = Q[metal species]/lH20] equation XV can be reduced to
Hunt et al.
/ Manganese(II)-Adenosine Diphosphate
4435
Table 111. Shift Data
-4.8 60.0 -5.1 119.8 129.5 138.5
0.053 0.963
0.053 0.961
0.002 0.644 0.002 0.988 0.993 0.996
11.1 & 1.0 44.1 f 1.0
12.3 f 1.0 60.1 f 1.5 5.4 f 1.9a 46.5 44.1 42.9
Average of at least three independent measurements. Errors are estimates. where H represents the measured shift in H z (V&d - VO). The Q values are related to the Qlim values by eq XI, thus eq XVI can be rewritten as
Table IV. Values of Qlim and na from Shift Data
Species MII(H~O)~~+
MnADPMn( ADP) 14-k PhbQb~,m[Mn(ADP)24-lh
Q~im
n
25.9 f 1.0 15.3 & 0.9 14.3 & 1 . 1
6.3 f 0.5 3.8 f 0.4 3.5 f 0.5
Normalized taking QMnlim= 24.5 k 1.1 for 6 waters and assuming A / h to be species independent.
+ PhMnQMnllm[Mn]h- PlmQml,,[MnADP-]l
1
- P I ~ Q ~ ~ ~ , , , [ M ~ ( A D-P )P~~~~- ~] IQ ~ ~ l , , , , [ M n(XVII) ll Values of P for MnADP- and Mn(ADP)24- were calculated from eq XI1 by using the results presented in Table 11. Similar values for Mn2+ were calculated from the results in Table V. The calculated values are given in Table 111. It should be noted that these P values are close to 1 a t the higher temperature and 0 at the lower temperature. In other words, slight imprecisions in the line-broadening data and results will have very little effect on the values of P since care has been taken to use temperatures where P is close to its limiting values. As with the line-broadening data, the species concentrations were calculated from the literature values of the stability constants and enthalpies cited above and from our calculated values of K2 and AH2. QMnllmwas taken to be 24.5 f 1.1 (Figure 1 ). With the calculated P's, the concentrations, and the shift data presented in Table 111, two simultaneous equations can be obtained from eq XVII. They have the form:
+ constantb~bli, + constantMn)
(XVIII)
The values of Qmlimand Qblimobtained from the solution of these equations are given in Table IV. The shift data for the aquo manganese system (solution 8) were treated in a similar manner. In this case eq XVIII can be further simplified to give
The value found for QMnlimis given in Table IV. Discussion Considering first the possible equilibria and species in the Mn(l1)-ADP system, the line-broadening interpretation (see Table 11) at two magnetic fields supports the existence of a bis complex with log K2 = ca. 2.6 a t 25 O C and AH2 = ca. -1 kcal/mol. This result is not unreasonable in the light of Frey and Stuehr's study4 of the nickel complexes. As can be seen from Table I the amount of bis complex can then be significant and caution must be used in interpreting data at high ligand concentrations (often used in N M R studies).
The data on solution 5 (low ligandimetal ratio) shows some deviation from the calculated values based on higher ligand/ metal ratios particularly at low field and low temperatures. The deviations do seem to be outside estimated errors, and a possible explanation could be formation of a Mn2(ADP) species analogous to that suggested as Mn2(ATP) by Mohan and Rechnitz.20 Further work on this could probably decide the issue. Turning to the question of the number of bound waters in the postulated species, we must draw upon the idea that the A/h value or the N M R shift of a bound water molecule is essentially independent of the number and kinds of other ligands present. The idea is supported at present for Mn(I1) by studies we have made on Mn(H20)62+, Mn(EDTA)(H20)2-, Mn(NTA)(H20)2-, Mn(Dacoda) (H20), and Mn(PhDTA)( H 2 0 ) 2where a variety of structures are involved. The shift per water is constant to f 1 0 % in these cases. This value corresponds to QMnlim= 24.5 for 6H2O bound or Alh = 6.0 MHz. In Table IV the n values obtained with the above considerations are given. For the mono Mn-ADP complex, 4 H 2 0 / M n appear to be present. This is consistent with two bound phosphate oxygens or one oxygen and the N-7 from the adenine ring but not simultaneous binding to the two phosphates and N-7. I n the case of M I I ( A D P ) ~ ( H ~ O ) ,n~ appears to be 3 or 4 rather than 2 as might have been the naive expectation. Several possible structures can be imagined. Considerable numbers of reports of stacking in the free nucleotides and their complexes exist.2' Examination of models suggests that a head-to-tail stacking22 of the ligands in the metal complex would permit two phosphates and one N-7 to bind to the metal leaving 3-4H20/Mn and perhaps explaining the fair stability apparent for the bis complex. As a check on our postulate of a bis complex we refit the data leaving K l , AHl, K2. and AH2 free to vary and obtained the same values within the experimental errors. We found, in addition, that adding a dimerization equilibrium for the free ligand led to the same fit first found with no dimerization (i.e., K dimer was
